Abstract
This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymptotically up to first order, each additive component can be estimated as well as it could be by a least squares estimator if the other components were known. The algorithm for the calculation of the estimator uses backfitting. Convergence of the algorithm is shown. Finite sample properties are also compared through simulation experiments.
Information
Published: 1 January 2007
First available in Project Euclid: 4 December 2007
zbMATH: 1176.62035
MathSciNet: MR2459939
Digital Object Identifier: 10.1214/074921707000000355
Subjects:
Primary:
62G07
,
62G20
Keywords:
additive regression
,
backfitting
,
isotone regression
,
oracle property
,
pool adjacent violator algorithm
Rights: Copyright © 2007, Institute of Mathematical Statistics
